ON SYMMETRIC LINEAR DIFFUSIONS
文献类型：期刊论文
| 作者 | Li, Liping2 ; Ying, Jiangang1
|
| 刊名 | TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
 |
| 出版日期 | 2019-04-15 |
| 卷号 | 371期号:8页码:5841-5874 |
| 关键词 | Symmetric one-dimensional diffusions Dirichlet forms regular Dirichlet subspaces representation theorem |
| ISSN号 | 0002-9947 |
| DOI | 10.1090/tran/7580 |
| 英文摘要 | The main purpose of this paper is to explore the structure of local and regular Dirichlet forms associated with symmetric one-dimensional diffusions, which are also called symmetric linear diffusions. Let (epsilon, F) be a regular and local Dirichlet form on L-2(I, m), where I is an interval and m is a fully supported Radon measure on I. We shall first present a complete representation for (epsilon, F), which shows that (epsilon, F) lives on at most countable disjoint "effective" intervals with an "adapted" scale function on each interval, and any point outside these intervals is a trap of the one-dimensional diffusion. Furthermore, we shall give a necessary and sufficient condition for C-c(infinity) (I) being a special standard core of (epsilon, F) and shall identify the closure of C-c(infinity) (I) in (epsilon, F) when C-c(infinity) (I) is contained but not necessarily dense in F relative to the epsilon(1/2)(1)-norm. This paper is partly motivated by a result of Hamza's that was stated in a theorem of Fukushima, Oshima, and Takeda's and that provides a different point of view to this theorem. To illustrate our results, many examples are provided. |
| 资助项目 | China Postdoctoral Science Foundation[2015LH0043] ; China Postdoctoral Science Foundation[2016M590145] ; Chinese Academy of Science ; NSFC[11688101] ; Key Laboratory of Random Complex Structures and Data Science ; Academy of Mathematics and Systems Science ; Chinese Academy of Sciences[2008DP173182] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000464034200022 |
| 出版者 | AMER MATHEMATICAL SOC |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/34437]  |
| 专题 | 应用数学研究所 |
| 通讯作者 | Li, Liping |
| 作者单位 | 1.Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, HCMS, RCSDS, Beijing 100190, Peoples R China |
| 推荐引用方式 GB/T 7714 | Li, Liping,Ying, Jiangang. ON SYMMETRIC LINEAR DIFFUSIONS[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,2019,371(8):5841-5874. |
| APA | Li, Liping,&Ying, Jiangang.(2019).ON SYMMETRIC LINEAR DIFFUSIONS.TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY,371(8),5841-5874. |
| MLA | Li, Liping,et al."ON SYMMETRIC LINEAR DIFFUSIONS".TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 371.8(2019):5841-5874. |
入库方式： OAI收割
来源：数学与系统科学研究院
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